I have been worked on the development of a general model for analysis of correlated binary data with Dr. James J. Chen at the National Center for Toxicological Research. We have introduced general over-dispersed binomial variates and compared them with the conventional prior-posterior type distributions. In the work, we showed that the new model is more general than the prior-posterior type models for the data having correlation. We also developed new methods to generate over-dispersed binomial variates. The models can be applied to reproductive and developmental toxicity data.